The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

The total number of numbers greater than $100$ and divisible by $5$,that can be formed from the digits $3, 4, 5, 6$,if no digit is repeated is:

There are $3$ girls in a class of $10$ students. The number of different ways in which they can be seated in a row such that no two of the three girls are together is

There are $10$ different letters of the English alphabet. If words of $5$ letters are formed using these letters,how many words can be formed such that at least one letter is repeated?

Number of different words that can be formed from all letters of the word $APPLICATION$ such that two vowels never come together is -

The number of ordered pairs $(r, k)$ for which $6 \cdot ^{35} C_{r} = (k^2 - 3) \cdot ^{36} C_{r+1}$,where $k$ is an integer,is: